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A112924
Number of nonisomorphic connected Y-graphs Y(n:i,j,k) with girth 6 on 4n vertices (or nodes) for 1<=i,j,k<=n.
3
0, 0, 0, 1, 3, 2, 3, 2, 5, 3, 6, 6, 4, 4, 8, 12, 9, 4, 12, 10, 11, 19, 10, 12, 15, 12, 14, 22, 15, 12, 20, 16, 18, 31, 18, 18, 24, 16, 20, 50, 21, 20, 28, 22, 23, 50, 27, 24, 32, 24, 26
OFFSET
3,5
COMMENTS
A Y-graph Y(n:i,j,k) has 4n vertices arranged in four segments of n vertices. Let the vertices be v_{x,y} for x=0,1,2,3 and y in the integers modulo n. The edges are v_{1,y}v_{1,y+i}, v_{2,y}v_{2,y+j}, v_{2,y}v_{2,y+k} and v_{0,y}v_{x,y}, where y=0,1,...,n-1 and x=1,2,3 and the subscript addition is performed modulo n.
REFERENCES
I. Z. Bouwer, W. W. Chernoff, B. Monson, and Z. Starr (Editors), "Foster's Census", Charles Babbage Research Centre, Winnipeg, 1988.
LINKS
J. D. Horton and I. Z. Bouwer, Symmetric Y-graphs and H-graphs, J. Comb. Theory B 53 (1991) 114-129.
EXAMPLE
Y(6:1,1,1) is the smallest Y-graph with girth 6.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Marko Boben (Marko.Boben(AT)fmf.uni-lj.si), Tomaz Pisanski and Arjana Zitnik (Arjana.Zitnik(AT)fmf.uni-lj.si), Oct 06 2005
STATUS
approved